Course overview
This course treats single neuron modeling, including molecular models of
channels and channel gating, Hodgkin-Huxley style models of membrane currents,
non-linear dynamics as a way of understanding membrane excitability, neural
integration through cable theory, and network computation. The goal of the
course is to understand how neurons work as biological computing elements and
also to give students experience with modeling techniques as applied to
complex biological systems.
The course meets Mondays, Wednesdays, and Fridays from 9:00-10:00 a.m. in
Hodson 213 and Tuesdays from 9:00-10:00 a.m. in Gilman 17 on the Homewood
campus. The MWF classes are lectures and the T classes are recitations where
homework will be discussed and help with questions provided; T classes are
required for undergraduates and optional for graduate students. The course is
taught by Eric Young, 505 Traylor at the Medical School, telephone
410-955-3164 (eyoung@jhu.edu); the T.A. is Mollie Marko, telephone (410)
614-3424 (molliemodels@gmail.com). TA office
hours will be on Mondays from 10AM-12PM in Clark 213 (if no one shows up
by 10:30AM office hours will be cancelled for the day unless a prior
appointment has been made). The prerequisites are mathematics through linear
algebra and differential equations and an introduction to neuroscience (e.g.
580.422, 080.205, or 080.304); introductory signal and system theory (e.g.
580.222 or 520.213-214) is helpful.
There is no required text, although Biophysics of Computation by C. Koch is
an excellent book that covers most of the material in the course. Foundations
of Cellular Neurophysiology by D. Johnston and S. Wu covers some of the
material in a more elementary fashion and P. Dayan and L.F. Abbott Theoretical
Neuroscience provides a more modern view of some topics. Several chapters from
Methods in Neuronal Modeling (2nd ed.) edited by C. Koch and I. Segev will be
used. An excellent and comprehensive book on membrane physiology is Ionic
Channels of Excitable Membranes, (3rd ed.) by B. Hille. This book covers ion
channels in more depth than those above; it is required reading for anyone
seriously interested in this subject. Additional references include the
following: G.M. Shepherd, The Synaptic Organization of the Brain (4th ed.) is
a good introduction to neural systems for persons with no previous experience.
S.H. Strogatz Nonlinear Dynamics and Chaos cover aspects of nonlinear dynamics
and network theory that will be discussed in the course; some material from
H.R. Wilson, Spikes Decisions and Actions will also be used. The book
Dynamical Systems in Neuroscience by E.M. Izhikevich provides a useful view of
2nd-order nonlinear systems of the type used in neuroscience. A good overview
of network theory is J. Hertz, A Krogh, and R.G. Palmer, Introduction to the
Theory of Neural Computation. Finally, J.J.B. Jack, D. Noble, and R.W. Tsien,
Electric Current Flow in Excitable Cells contains detailed discussions of
older work, especially useful for cable theory. All of these are on reserve in
Eisenhower library.
Weekly homework assignments will be given. Solutions should be handed in
and will be graded. Two computer modeling projects will be assigned during the
term. The grade for graduate students will be based on the midterm (20%),
final (30%), the modeling projects (40%), and the homework (10%).
Undergraduates grades will be based on the midterm (30%), first modeling
project (30%), final (30%), and homework (10%). Students are encouraged to
discuss homework problems with colleagues, but the final product that is
handed in should be the student's own work. Modeling projects must be done
individually. A conscientious homework record will contribute to raising
marginal grades.
Course schedule
Updated August 29, 2011
Lectures are MWF 9-10 in Hodson 213. Parentheses
indicates no class meeting on that day.
Aug.
29, 31, Sept. 2 Introduction;
review of neurophysiology and thermodynamics; equilibria, electrodiffusion.
Sept.
(5), 7, 9 (Labor day), I-V
relationships; cellular steady state. Biological membranes and channels
12, 14, 16 Kcsa and similar channels. Barrier models of channel
permeation.
19, 21, 23 Voltage clamp analysis, gating; Hodgkin-Huxley and similar
models; simulation methods.
26, 28, 30 Phase-plane
analysis of nonlinear systems; model reduction, equilibrium points.
Oct.
3, 5, 7 Linearization,
classification of behavior near equilibrium points; limit cycles, bursting
(10),
11, 12, 14 Role of calcium;
varieties of channels; neuromodulation (Class on the 10th is moved to the 11th
for fall break). MIDTERM EXAM OCT 14, 2011
17, 19, 21 Examples of channel systems; corticothalamic neurons;
regulation of ion channel density. Dendritic trees, distribution of inputs on
dendrites
24, 26, 28 Cable equation
for dendritic trees, finite cylinders, the equivalent cylinder.
FIRST MODELING PROJECT DUE OCT. 28, 5:00
P.M.
Oct.
31, Nov. 2, 4 Rall motorneuron
model; dendritic tree inverse problems; compartmental models.
7, 9, 11
Real dendritic trees, synaptic coupling to the soma, arrangement of
synapses.
14,
16, 18 Spines and calcium;
plasticity.
21, (23, 25) Neural
integration (Thanksgiving vacation).
28, 30, Dec. 2 Neural
networks; Stability of network fixed points; network dynamics. Liapunov
functions and the Cohen-Grossberg theorem.
Dec.
13 FINAL EXAM 9-12 AM.
SECOND MODELING PROJECT DUE DEC 19, 5:00 P.M.
Homeworks
Homework assignments will be given weekly, and are generally due on Fridays by
the end of class. They can be submitted in class or dropped off to the TA
(notify TA if doing so). Homework will not be accepted after solutions are
posted. The links below will return pdf files of the homework sets and
solutions. The pdf files can be viewed with the free Adobe
Acrobat Reader. Solution sets will be available for downloading after the
due-date of the homework.
Course notes
Class lectures
Other relevant notes
Modeling projects
Two computer modeling projects will be assigned. All work on the modeling
projects must be done individually.
|
Project #1 : Due October 28, 2011 by 5:00
P.M. For students
in 580.439 (undergraduates), preliminary answers to parts 1-6 are due in class on Oct 17. Matlab files 2011 *UPDATED mlodejac 10/23/2011 mlodejac *UPDATED mlodejac 10/23/2011 |
|
Project #2 : Due December 19, 2011 by
5:00 P.M. (email pdf to eyoung@jhu.edu) Project proposal due on Monday, November 14, 2011 |
Previous exams
Copies of previous midterms and finals are posted below, along with solutions.
| Midterm exam, 2011 | Midterm exam solutions 2011 |